For the guy I knew who was into flat earth, the signal was that the scientific establishment sometimes lied to him and he didn't have the resources to know when it was and wasn't telling the truth. He didn't seem that interested in the fact that I, a friend he trusted completely, did have those resources in this specific case. Given that behavior, I am not sure how much he really believed the earth was actually flat. Even if he didn't trust the system, he should have been able to trust me. That leads me to think it was about the system, not the literal truth of the matter. It was a statement of distrust in the face of an inability to personally verify, an attitude many of us share when it comes to such things as governments and corporations. It is perfectly true that the scientific establishment does get it wrong sometimes, which must be very creepy when you know you can't tell. For this individual, I think flat earth was an objection and a demonstration of how much trust had been lost and how powerless he was and how impossible it was to establish belief without trust even in such a simple case.
I think the topic of the flat earth, like the topic of the faked moon landings, is not chosen because the evidence is particularly convincing in these cases. It is a shot directly at things perceived to be sacred to science. An insult out of rebellion, not an intellectual assessment of the sufficiency of evidence. I do wonder how much of this psychology plays into the vaccine issue, that also having big elements of perceived sacredness to the distrusted establishment.
Anyway, this is is not the only person I know who is into such egregiously anti-scientific theories. I can think of one other guy in the same boat, and he also is coming from a similar psychological place: not that smart, not that well educated, knows beyond a shadow of a doubt that the establishment sometimes lies, chooses intellectual rebellion over powerlessness. I am not sure how seriously he believes this stuff either. I am not sure he even knows. I don't think that's the point.
There certainly is a truth to the creepiness of both the intellectual power imbalance and the occasional betrayal of trust. I can feel it too, in fields I don't have time to critique closely.
And indeed, even for those of us who don't go quite so far as to shake our fist in defiance and declare unbelief, the idea of this power imbalance being both extreme and sometimes possibly sinister is so well embedded in the consciousness that it is a recurring trope in our mythology. Dangerous, possibly sinister scientific research, hidden from the public by either lies or intellectual impenetrability, is an extremely common premise in fiction. It reflects this same reality. Perhaps we keep it to fiction, but the stories wouldn't work if we didn't feel it too. A thousand years ago, in Beowulf, Grendel is the product of a curse from God. That made a story work back then. Our monsters now escape from government labs. This tells you something about us, about something we all sort of seriously perceive and fear.
This is the signal behind the conspiracy.